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In the figure, PA is tangent to semicircle SAR, PB is tangent to semicircle RBT, and SRT is a straight line. If arc AS is 63 degrees and arc BT is 42 degrees, then find angle APB, in degrees.

 

 Nov 1, 2020
 #1
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Let midpoints of SR and RT be M and N

 

MAP and NBP are right angles

 

∠AMS = 63º              ∠BNT = 42º

 

AMNBP is a pentagon         (sum of interior angles of a pentagon is 540º) 

 

∠APB = 540 - (180 + 117 +138) = 105º

 Nov 1, 2020

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